Bayesian spatial prediction

This paper presents a complete Bayesian methodology for analyzing spatial d ata, one which employs proper priors and features diagnostic methods in the Bayesian spatial setting. The spatial covariance structure is modeled usin g a rich class of covariance functions for Gaussian random fields. A genera l class of priors for trend, scale, and structural covariance parameters is considered. In particular, we obtain analytic results that allow easy comp utation of the predictive distribution for an arbitrary prior on the parame ters of the covariance function using importance sampling. The computations , as well as model diagnostics and sensitivity analysis, are illustrated wi th a set of precipitation data.